Journal ArticleDOI
Epistemological Investigation of Classroom Interaction in Elementary Mathematics Teaching.
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In this paper, the authors investigated the problem of meaning development in everyday teaching and developed and discussed decisive requirements for the maintenance of an interactive constitution of meaning for mathematical knowledge for second-grade students.Abstract:
In everyday teaching, the mathematical meaning of new knowledge is frequently devalued during the course of ritualized formats of communication, such as the “funnel pattern”, and is replaced by social conventions. Problems of understanding occurring during the interactively organized elaboration of the new knowledge require an analysis of the interplay between the social constraints of the communicative process and the epistemological structure of the mathematical knowledge. Specific aspects of the problem of meaning development are investigated in the course of two exemplary second-grade teaching episodes. These are then used to develop and discuss decisive requirements for the maintenance of an interactive constitution of meaning for mathematical knowledge.read more
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The challenge of developing statistical literacy, reasoning and thinking
Dani Ben-Zvi,Joan Garfield +1 more
TL;DR: This chapter discusses the development of Instructional Design for Supporting the Development of Students' Statistical Reasoning and research on Statistical Literacy, Reasoning, and Thinking.
Book
Design research in statistics education : on symbolizing and computer tools
TL;DR: The research presented in this thesis is a sequel to design research carried out by Cobb, McClain, and Gravemeijer (2003) and aims at contributing to an empirically grounded instruction theory for early statistics education in which educational computer tools are used.
Journal Article
Un enfoque ontológico y semiótico de la cognición matemática
TL;DR: In this article, the authors describe a technique to analyse mathematics teaching and learning processes, which permits the characterisation of the institutional and personal meanings involved and the identification of possible semiotic conflict in the didactic interaction.
Book ChapterDOI
Learning to reason about distribution
Arthur Bakker,Koeno Gravemeijer +1 more
TL;DR: The development of reasoning about distribution in seventh-grade classes is described in three stages as students reason about different representations, and it is shown how specially designed software tools, students’ created graphs, and prediction tasks supported the learning of different aspects of distribution.
Journal ArticleDOI
The array representation and primary children’s understanding and reasoning in multiplication
TL;DR: In this article, the authors examine whether the array representation can support children's understanding and reasoning in multiplication, and find that it can help children to understand and reason in multiplication problems, and that it may even improve their performance.
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Journal Article
Über Sinn und Bedeutung
TL;DR: In this article, a=a and a=b sind offenbar Satze von verschiedenem Erkenntniswerte: a =a gilt a priori und ist nach Kant analytisch zu nennen.
Journal ArticleDOI
Where Is the Mind? Constructivist and Sociocultural Perspectives on Mathematical Development
TL;DR: The authors argue that the sociocultural perspective informs theories of the conditions far the possibility of learning, whereas theories developed from the constructivist perspective focus on what students learn and the processes by which they do so.
Book
The Invention of Culture
TL;DR: Wagner argues that culture is not a given that shapes the lives of the people who share it, but rather, it is people who shape their culture by constantly manipulating conventional symbols taken from a variety of everchanging codes to create new meanings as mentioned in this paper.